Bi-objective optimization for the project scheduling problem with variable resource availability

Resource shortage is usually one of the most important reasons for the project delay. Then project managers tend to consider increasing the resource availability for shortening the project makespan. However, this will lead to an increased project cost. So, the trade-off between the project makespan and cost is needed. Suppose the renewable resource availabilities are variable and expressed by internal numbers, then a multi-mode resource constrained project scheduling model is constructed for minimizing both the project makespan and cost. Based on the non-dominated sorting genetic algorithm II, a hybrid algorithm including the preprocessing of the resource availability's upper bound and the cost improvement for feasible schedules, is designed to obtain Pareto-optimal solutions. The effectiveness of the model and algorithm is proved by solving both the example project and a set of projects generated by ProGen. Finally, through analyzing the results of an adapted construction project, the necessity of finding out the Pareto-optimal set is demonstrated. The optimization results can provide basis for decision makers to make better decisions.